This paper proposes a constrained clustering method that is based on a graph-cut problem formalized by SDP (Semi-Definite Programming). Our SDP approach has the advantage of convenient constraint utilization compared with conventional spectral clustering methods. The algorithm starts from a single cluster of a complete dataset and repeatedly selects the largest cluster, which it then divides into two clusters by swapping rows and columns of a relational label matrix obtained by solving the maximum graph-cut problem. This swapping procedure is effective because we can create clusters without any computationally heavy matrix decomposition process to obtain a cluster label for each data. The results of experiments using a Web document dataset demonstrated that our method outperformed other conventional and the state of the art clustering methods in many cases. Hence we consider our clustering provides a promising basic method to interactive Web clustering.